# The existence of higher logarithms

Journal Article (Journal Article)

In this paper we establish the existence of all higher logarithms as Deligne cohomology classes in a sense slightly weaker than that of [13, Sect. 12], but in a sense that should be strong enough for defining Chem classes on the algebraic K-theory of complex algebraic varieties. In particular, for each integer p ≥ 1, we construct a multivalued holomorphic function on a Zariski open subset of the self dual grassmannian of p-planes in ℂ2p which satisfies a canonical 2p + 1 term functional equation. The key new technical ingredient is the construction of a topology on the generic part of each Grassmannian which is coarser than the Zariski topology and where each open contains another which is both a K (π, 1) and a rational K (π, 1). © 1996 Kluwer Academic Publishers.

### Duke Authors

### Cited Authors

- Hain, RM

### Published Date

- December 1, 1996

### Published In

### Volume / Issue

- 100 / 3

### Start / End Page

- 247 - 276

### International Standard Serial Number (ISSN)

- 0010-437X

### Citation Source

- Scopus